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arXiv · 2103.07809

Fooling Gaussian PTFs via Local Hyperconcentration

Ryan O'Donnell·Rocco A. Servedio·Li-Yang Tan·Daniel Kane
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Abstract

We give a pseudorandom generator that fools degree-$d$ polynomial threshold functions over $n$-dimensional Gaussian space with seed length $\mathrm{poly}(d)\cdot \log n$. All previous generators had a seed length with at least a $2^d$ dependence on $d$. The key new ingredient is a Local Hyperconcentration Theorem, which shows that every degree-$d$ Gaussian polynomial is hyperconcentrated almost everywhere at scale $d^{-O(1)}$.

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Ryan O'Donnell, Rocco A. Servedio, Li-Yang Tan, Daniel Kane. 2021-03-13. Fooling Gaussian PTFs via Local Hyperconcentration. https://arxiv.org/abs/2103.07809

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